ńņš. 13 |

Consider two ļ¬rms. A has a E(gE ) = 5% growth rate and earnings of $100 (next year); and B

Ė The average of

individual P/E ratios is

has a E(gE ) = 14% growth rate and earnings of $50 (next year). Both have an E(Ė) = 15% cost

r

Ė not the overall P/E ratio

of capital. Their respective values should be

$100

P/E =

PA ā” VA = = $1, 000 ā’ 10 ,

15% ā’ 5%

(10.19)

$50

P/E = 100 .

PB ā” VB = = $5, 000 ā’

15% ā’ 14%

What would happen if these two ļ¬rms merged into a single conglomerate, called AB? Assume

AB does not operate any diļ¬erentlyā”the two ļ¬rms would just report their ļ¬nancials jointly. AB

must be worth $6,000ā”after all, nothing has changed, and you know that NPVs are additive. It

would have earnings of $150. Thus, its P/E ratio would be $6, 000/$150 = 40.

PAB (10.20)

= 40 ā’ PAB = 40 Ā· EAB .

Correct But Unknown AB P/E ratio:

EAB

Your goal is to value AB. Fortunately, you just happen to know a perfectly comparable ļ¬rm for

division A (trading at about P/E = 10), and a perfectly comparable ļ¬rm for division B (trading

at about P/E = 100). You even have a good idea of the relative size of the divisions inside

AB (5:1). Knowing the combined earnings of AB of $150, you want to estimate a value for AB,

based on your two comparables. Unfortunately, neither the unweighted average P/E ratio nor

the weighted average P/E ratio gives you the correct desired P/E ratio of 40:

PA PB

1 1

Ā· + Ā· = 55 ,

Unweighted P/E ratio Average of A and B

EA EB

2 2

(10.21)

PA PB

1 5

Ā· + Ā· = 85 .

Weighted P/E ratio -Average of A and B

EA EB

6 6

Applying either of these two P/E ratios to your $150 in earnings would result in price assess-

ment for AB that would be too high.

Important:

ā¢ Price-earnings ratios cannot be averaged.

ā¢ Mergers change the P/E ratio, even if they do not create value.

The inability to aggregate divisions is not only an issue for the ļ¬rm that is to be valued, but it also Lack of easy aggregation

makes it difļ¬cult to

makes it diļ¬cult to extract a single comparable ratio from a division from inside conglomerates.

value even well-deļ¬ned

In our case, letā™s assume that you only wanted to value the U.S. Dr. Pepper division, and that ļ¬rms, if the comparables

the U.S. Coca-Cola soda division was a perfect comparable for the U.S. Dr. Pepper. But how do are divisions inside

larger ļ¬rms.

you extract a P/E ratio for the Coca-Cola division, if all you know is the P/E ratio of the overall

Coca Cola company with all its international subsidiaries, Minute Maid, Odwalla, etc.?

ļ¬le=comparables.tex: LP

248 Chapter 10. Valuation From Comparables.

You have no good methods to aggregate and disaggregate P/E ratios. Therefore, strictly speak-

The consequences of the

aggregation failure ing, you can only compare full ļ¬rms that are similar, which means that P/E ratios are likely

mean, strictly speaking,

to work well only for simple and well-deļ¬ned companies, and not so well for complex con-

that only the most basic

glomerates. In retrospect, it would have been a coincidence if your naĆÆve attempt to apply the

single-product ļ¬rms

should be compared.

overall P/E ratio of Coca Cola or PepsiCo to Cadbury Schweppesā™s overall earnings would have

worked. Indeed, in retrospect, it was an amazing coincidence that PepsiCo and Coca Cola had

such similar P/E ratios. We lived in blissful ignorance.

In Part III, we will introduce āmarket-betaā as a valuation measure. Unlike P/E ratios,

market-beta nicely aggregates and disaggregates. This makes it relatively easy to com-

pute betas for conglomerates from their divisions, and to extract a division beta (given

the conglomerate beta and comparable betas for other divisions).

10Ā·3.C. A Major Blunder: Never Average P/E ratios

On top of these unavoidable P/E ratio problems, many an analyst has mistakenly created a

Using a ļ¬rm with

negative earnings as the much worse and avoidable problem by averaging P/E ratios. Averaging overlooks the fact that

comparable makes

earnings can be (temporarily) zero or negative, which can totally mess up any P/E ratio analysis.

absolutely no sense.

For example, consider the example where the choice of industry comparables for X consists of

A and B.

Value (P) Earnings (E) P/E ratio E/P yield

+$10 ā’

Firm A $1,000 100 1.000%

ā’$5 ā’ ā’4 ā’0.250%

Firm B $20

Industry Average: 48 0.375%

Firm X ? $2

If Firm B were the only comparable, it would imply a negative value for Firm X,

(10.22)

VX = EX Ā· (PB /EB ) = $2 Ā· (ā’4) = ā’$8 .

A value of minus eight dollars for a ļ¬rm with positive earnings and limited liability is not

sensible. Luckily, this comparables-derived valuation is so nonsensical that no analyst would

not notice it.

But the problem is often overlooked when an analyst uses a P/E industry average. For example,

Averaging P/E ratios can

look reasonable at ļ¬rst assume our analyst uses an average of both comparables: Firm A has a P/E ratio of 100, Firm B

glance...

has a P/E ratio of ā’4. Thus, the average P/E ratio would be 48 (= [100 + (ā’4)]/2), which is a

reasonable looking average that would not raise a red ļ¬‚ag. A thoughtless analyst could conclude

that Firm X should be worth VX = EX Ā· (PA,B /EA,B ) = $2 Ā· 48 = $96.

Figure 10.4 makes the absurdity of this method even clearer. What happens to the implied value

...but it is not.

of Firm X if Firm Bā™s earnings change? As Firm B improves its performance from about ā’$5

to about ā’$1, the average P/E ratio becomes 40, and your implied value remains a seemingly

reasonable $80. Beyond ā’$1, earnings improvements in the comparable B create non-sensically

huge negative implied ļ¬rm values for X. Then, further improvements suddenly create non-

sensically huge positive ļ¬rm values. Finally, once the earnings of B are above $1 or so, you

again get seemingly reasonable values (of about $100) for X. So, small changes in earnings

can produce either seemingly sensible or non-sensible valuations. In other examples, even one

comparable with earnings close to zero among a dozen comparables can totally mess up an

average of many comparable P/E ratios.

ļ¬le=comparables.tex: RP

249

Section 10Ā·3. Problems With P/E Ratios.

Figure 10.4. Implied Value vs. Earnings Changes of One Comparable

300

Implied Value of Firm X

200

100

0

ā’100

ā’10 ā’5 0 5 10

Earnings of Comparable B

If the earnings of the comparable B are $1, you get a sensible value for your ļ¬rm X. If the earnings are a little bit lower,

you get a non-sensically high number; if the earnings are a little bit lower, you get a non-sensically low number; and

if the earnings are yet a little bit lower, you again get a non-sensical numberā”but one that can appear at ļ¬rst glance

to be of reasonable magnitude.

In an eļ¬ort to deal with this problem, a common industry practice is to drop out ļ¬rms with Excluding ļ¬rms does not

help.

non-positive earnings from P/E averages. Unfortunately, this is not a good solution, either. First,

you want an accurate valuation, and the stock market did value Firm B at $20. You have no

good reason to ignore ļ¬rms with low earnings. Second, dropping out some ļ¬rms does not

solve the problem: the ļ¬rm would enter the P/E average if its earnings are +5 cents (leading to

a very high industry P/E average), but be dropped out if its earnings are ā’5 cents (potentially

leading to a much lower industry average). A small change in the P/E ratio of one comparable

among the industry would have a disproportionately large impact on comparables valuation

due to arbitrary inclusion/exclusion of comparables, rather than to closeness of earnings to

zero. The reason for all these problems with price-earnings ratios is that earnings are in the

denominator. The function 1/E is both discontinuous and very steep when earnings are close

to zero. In contrast, the price (value) is guaranteed to be positive.

Fortunately, there are two easy overall alternatives to obtain good āpseudo averaged P/E ratios,ā The two better

alternatives.

even if some ļ¬rmsā™ earnings in the industry are low:

1. Work with earnings yields (E/P yields) instead of P/E ratios.

In the example, the E/P yield of Firm A is $10/$1, 000 = 1%; the E/P yield of Firm B

if it earned ā’1 cent is ā’$0.01/$20 = ā’0.05%. The average E/P yield is thus [1% +

(ā’0.05%)]/2 = 0.475%. Inverting this back into a P/E ratio provides a halfway sensible

value for the P/E ratio (1/0.475% ā 211).

2. Add up all market capitalizations in the industry and all earnings in the industry, and

then divide the two.

In the example where B earned ā“1 cent, the total industry earnings would be $10.00 ā’

$0.01 = $9.99, the entire industry market value would be $1, 000 + $20 = $1, 020, and

ļ¬le=comparables.tex: LP

250 Chapter 10. Valuation From Comparables.

the average P/E ratio would be $1, 020/$9.99 ā 102. Note that in this method, ļ¬rms are

not equally weighted, but weighted by their relative market valuation. This may or may

not be desirable: In our example, ļ¬rm A would become the dominant determinant of your

comparable valuation ratio.

Neither of these methods will give a very appealing comparable if the total industry average

earnings are very small or negative. Our averaging alternatives can only avoid the problem of

excessive inļ¬‚uence of a small number of negative (or small) earnings ļ¬rm in the average.

Important: Although neither P/E ratios nor E/P yields can be averaged, strictly

speaking, an averaging-like operation can often be performed. We do so only

because we lack a better alternative and we do not want to rely on just one single

comparable. Never directly average P/E ratios. Instead

1. Either average E/P yields and then invert,

2. or divide total P sums by the total E sums.

Never take these averages literally. Your goal must be to produce an āintuitively

good (industry) averageā derived from multiple comparables, not an exact number.

You may judge your estimation to be better if you omit outlier ļ¬rms, for example.

10Ā·3.D. Computing Trailing Twelve Month (TTM) Figures

There is one āsmallā mechanical detail left: Timing. First, is it meaningful to use annual earnings

When comparable ļ¬rms

report annual for a ļ¬rm if the last annual report was from eleven months ago? Or should you use just the last

statements in different

quarterā™s numbers? Second, some ļ¬rms report earnings in June, others in December. Should

months, the time change

you compare ļ¬nancials that are timed so diļ¬erently, especially if the economy has changed

in economic climate

introduces yet another

during this time lag? For example, consider the following reports:

problem.

2001 2002

Q1 (Mar) Q2 (Jun) Q3 (Sep) Q4 (Dec) Q1 (Mar) Q2 (Jun) Q3 (Sep)

Comparable Firm $1 $2 $3 $9 $5 $6 $7

ā’ Ann:$15

Your own ļ¬rm is closing its ļ¬nancial year with annual earnings of $12 in October 2002. What

are the relevant comparable earnings? Should you compare your own annual earnings of $12

to the dated annual earnings of $15 from December 2001?

Anecdote: What P/E ratio to believe?

Exchange traded funds (ETFs) are baskets of securities, often put together to mimick an index. You can think

of ETFs as ļ¬rms for which you know the valueā”and price earnings ratioā”of each and every division (stock

component).

On March 13, 2006, the WSJ reported that Barclays Global Investors calculates the P/E ratio of its iShares S&P500

ETF as 16.4 and that of its iShares Russell 2000 ETF as 19.1. The Russell 2000 includes many mid-market ļ¬rms.

It has garnered nearly $7.5 billion from investors, and is one of the fastest growing funds in 2006. So, the two

funds look comparable in value and/or riskā”or do they?

If you compute the weighted sum of the market value of all stocks in the Russell 2000 index and divide that

ļ¬gure by the companiesā™ total earnings, you ļ¬nd that this ETF has a P/E Index of 41. Why the diļ¬erence?

Because the iShares ETF excludes all loss-making companies when calculating the measureā”and there were

many Russell 2000 components thus excluded. Karl Cheng, an iShares portfolio manager, says investors donā™t

normally look at negative P/E ratios for companies, so they donā™t include it in the data. Investors should consider

other measures, he says. Thanks, Karl!

Source: Wall Street Journal, March 13, 2006 (page C3).

ļ¬le=comparables.tex: RP

251

Section 10Ā·3. Problems With P/E Ratios.

You could try to work directly with quarterly earnings, but this is usually not a good idea. Most This time difference can

be reduced, even though

ļ¬rms do more business in December, and December can be the ļ¬rst month in a quarter or the

quarterly accounting

last month in a quarter. Not only are diļ¬erent quarters diļ¬cult to compare across ļ¬rms, but statements themselves

the fourth quarter may be diļ¬cult to compare even to the other three quarters of the same ļ¬rm. should be avoided.

Instead, use quarterlies

So, generally, the best method to adjust ļ¬‚ows (such as earnings) into a āmost recent annualized

and annuals to compute

equivalentā is to use a trailing twelve months (TTM) adjustment. In our example, this means ātrailing twelve monthā

(TTM) ļ¬gures.

adding the earnings from Q4-2001 through Q3-2002,

As If Annual in Sep 2002 = $9 + $5 + $6 + $7 = $27

(10.23)

= Q4-01 + Q1-02 + Q2-02 + Q3-02 .

TTM Earnings

Using the reported earnings, you can also compute this

As If Annual = + ($5 ā’ $1) + ($6 ā’ $2) + ($7 ā’ $3) = $27

$15

TTM Earnings = Ann-01 + (Q1-02 ā’ Q1-01) + (Q2-02 ā’ Q2-01) + (Q3-02 ā’ Q3-01) .

(10.24)

There are two caveats: ļ¬rst, TTM adjusts only āļ¬‚owā numbers (such as earnings or sales), āTrailing twelve monthsā

only works for āļ¬‚owā

never āstockā numbers (such as corporate assets). Stock numbers are whatever they have been

numbers (such as

reported as most recently. Second, ļ¬rms sometimes change their ļ¬scal year, often to make it income), not for stock

intentionally more diļ¬cult to compare numbers. In this case, extra care must be exercised. numbers (such as

assets).

10Ā·3.E. Leverage Adjustments For P/E Ratios

This section assumes that riskier projects have to offer higher expected rates of return.

Why this is the case will only fully become clear in Part III. Trust me for now.

Companies can be ļ¬nanced through a mix of debt and equity. You would want to know if Does leverage inļ¬‚uence

P/E ratios?

the P/E ratio of a ļ¬rm is changed by its leverage. If the same ļ¬rm with more debt in its capital

structure has a diļ¬erent P/E ratio, then you cannot compare two otherwise identical companies

with diļ¬erent debt ratios without adjustment.

Return to a simple example. With $100 in annual earnings, a growth rate of 0% now, and an Recapitalizing a 100-0

ļ¬rm into a 50-50 ļ¬rm.

appropriate cost of capital of 10%, a hypothetical ļ¬rm A would be worth $1,000. A has no

debt (leverage). We now work out what happens to the price-earnings ratio of A if it were to

recapitalize itself. That is, A takes on a loan of $500, and pays the cash proceeds from the loan

to the equity share owner. This is called a debt-for-equity (or debt-for-stock) exchange. Such

transactions are fairly common.

From Chapter 5, you already know that the cost of capital (interest rate) consists of multiple ...with different costs of

capital for bonds and

components: the time-premium, the default-premium (on average, zero), and the risk-premium.

stocks.

From Chapter 5Ā·3.B, you know that levered equity is riskier than debt. Also, trust me now when

I claim that if investors are not risk-neutral, the cost of capital is generally higher for riskier

securities. The expected rate of return on risky investments must be higher than the expected

rate of return on safer investments; it must be higher for equity than for debt; and it must be

higher for riskier debt than for safer debt. In the example in this section, we shall assume that

the appropriate expected rate of return for a ļ¬rm ļ¬nanced with 50% debt is 7.5% for the debt,

and 12.5% for the remaining 50% ālevered equityā (residual ownership).

ļ¬le=comparables.tex: LP

252 Chapter 10. Valuation From Comparables.

The cost of capital for the ļ¬rm overall remains at 10% after the ļ¬rm is ļ¬nanced diļ¬erently,

Side Note:

because

Ā· + Ā· =

50% 7.5% 50% 12.5% 10%

(10.25)

proportion cost of capital proportion cost of capital cost of capital

Ā· + Ā· = .

of debt for debt of equity for equity for the ļ¬rm

The cost of capital for the overall company has not changed. Section 21 will discuss this in more detail.

Figure 10.5. Earnings, Interest Payments, and Price-Earnings ratios as a Function of Leverage

10.0

100

Earnings and Interest Payments

9.5

Ear

nin

80

gs

Price/Earnings Ratio

9.0

60

8.5

8.0

40

nts

7.5

me

20

ay

st P

ere

Int

7.0

0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Debt/Asset Ratio Debt/Asset Ratio

As the ļ¬rmā™s debt ratio goes up, its interest payments increase, its earnings decreaseā”and so does its price-earnings

ratio. The same underlying projects can thus have a price-earnings ratio of, say, 7 or 10.

How much total interest payment does the debt have to promise? The loan value is $500, the

The changed

price-earnings ratio interest rate is 7.5%, and payments are forever. Therefore, the perpetuity formula can be solved

under the 50-50 capital

as follows:

structure.

Annual Payment

Annual Payment = $37.50/year

$500 = ā’

7.5%

(10.26)

CF

= .

PV

E (r )

Having issued debt, the equity no longer receives $100 per year, but only what is left after

interest payments, i.e., $100 ā’ $37.50 = $62.50 per year. Consequently, the price-earnings

ratio of this ļ¬rmā™s equity shares will be the value of the equity (now $500) divided by the

earnings available to equity,

(10.27)

P/E = $500/$62.50 = 8.0 (times) .

In sum, when the same ļ¬rm is ļ¬nanced with a 50/50 debt equity ratio, rather than a 0/100

debt equity ratio, its price-earnings ratio is 8 rather than 10. Figure 10.5 shows this graphically

for a whole range of diļ¬erent debt-asset ratios: the higher the ļ¬rmā™s debt load, the higher the

interest payments, the lower the equity earnings, and the lower the price-earnings ratio. (The

ļ¬gure assumes that the expected [not just the promised!] debt interest rate increases in the

debt-asset ratio according to the formula 5% + 5% Ā· D/A.)

Important: The price-earnings ratio is higher when the ļ¬rm has lower leverage

(debt-equity ratio).

ļ¬le=comparables.tex: RP

253

Section 10Ā·3. Problems With P/E Ratios.

To compare ļ¬rms that you deem to be identical in operations, but diļ¬erent for their capital Revisiting CocaCola,

PepsiCo, and Cadbury:

structures, you need to adjust them to equivalent, unleveraged values. Let us put this insight

Using leverage

to practical use. Assume that the companies of Coca Cola, PepsiCo, and Cadbury Schweppes information to improve

are identical, even if their equities may not be because of their diļ¬erent leverage ratios. Some valuation.

gathering of information from Yahoo!Finance allows you to put together Table 10.3:

Table 10.3. Financial Information from Yahoo

Leverage Financials, in billion-$

D

Equity

Interest Earn-

D+E

P/E = D/A

STOCK (SYM) D/E Expense EBITDA ings Value

Coca Cola (KO) 35 56% 36% $0.244 $6.14 $3.91 $136.85

PepsiCo (PEP) 34 33% 25% $0.207 $4.26 $2.74 $93.16

Cadbury Schweppes (CSG) 21 49% 33% $0.155 $1.28 $0.72 $15.12

Note: The ļ¬rmā™s asset value A is the sum of its equity value E and debt value D. The formula to translate debt-equity

(D/E) ratios into debt-asset (D/A) ratios is

D+E E D

1 1 1

= = = 1+ ā’ = . (10.28)

D/ D/ 1

D D E ā’1

(D + E)

A D/A

In general, debt-equity ratios could either be based on the market value of equity or the book value of equity. The

latter is especially problematicā”though commonly used.

You are now ready to ask what would happen if the three companies were not leveraged, but Translating P/E ratios of

levered ļ¬rms into

were ļ¬nanced only by equity. First, the earnings would not be diminished by the interest

P/E ratios as if unlevered.

expense that the ļ¬rms are currently paying. You must add back the interest expense to the

earnings to get āas if unleveredā earnings. Second, the market capitalization of equity would

increase. After all, the ļ¬rmā™s projects would no longer be ļ¬nanced by debt and equity, but by

equity alone. If a ļ¬rm has a debt/equity ratio of 33% (1/3), for every dollar worth of debt it

currently has 3 dollars worth of equity. Thus, an unlevered equivalent ļ¬rm would be ļ¬nanced

with $4 in equity. To convert a debt/value ratio to an unlevered value, divide the (levered) equity

value by one minus the debt/value ratio. In Table 10.4, we can construct āas if unleveredā P/E

ratios by dividing the unlevered ļ¬rm capitalization by the unlevered equity earnings (all quoted

in billion dollars):

Table 10.4. Computing Unlevered P/E Ratios

STOCK (SYM) (P/E)Lv (P/E)UnLv

Unlevered Earnings Unlevered Value

$3.91 + $0.244 = $4.15 $136.85/(1 ā’ 36%) ā $214

Coca Cola (KO) 35 52

$2.74 + $0.207 = $2.95 $93.16/(1 ā’ 25%) ā $124

PepsiCo (PEP) 34 42

$0.72 + $0.155 = $0.88 $15.12/(1 ā’ 33%) ā $23

Cadbury (CSG) 21 26

These computations are only approximations and wrong for at least two reasons. First, we

Side Note:

assume no taxes. If by unlevering the ļ¬rm incurred more taxes, these taxes should be subtracted from ļ¬rm

value. Chapter 22 will discuss the role of corporate taxes in more detail. Fortunately, in this particular case (for

these three companies), not much would change. Second, the unlevering depends on assuming that the ļ¬rm

continues forever, so that the perpetuity formula is applicable. This could also be wrong. Again, fortunately, in

this particular case (for these three companies), not much would change for other growth assumptions.

ļ¬le=comparables.tex: LP

254 Chapter 10. Valuation From Comparables.

Does it appear as if Cadbury Schweppes (the underlying unlevered company) now is a lot more

Unfortunately, in our

case, after proper like PepsiCo than levered Cadbury Schweppes shares were to levered PepsiCo shares? Unfortu-

adjustment, the

nately, the answer is the opposite of what you should have hoped for. The P/E ratios of Cadbury

P/E ratios have become

Schweppes are even more diļ¬erent from those of Coca Cola and PepsiCo than they were before.

more different, not

more similar.

You also have some more information to evaluate your earlier remarkable ļ¬nding that PepsiCo

could be accurately valued with the comparable of Coca Cola. You chose Coca Cola because

you believed that the ļ¬rm of Coca Cola would be similar to PepsiCo, not that the equity shares

of Coca Cola would be similar to those of PepsiCo. But, in this case, the ļ¬rms of Coca Cola

and PepsiCo are less similar than the equity shares of Coca Cola and PepsiCo: their unlevered

P/E ratios are farther apart than their levered P/E ratios. So, if you had properly applied the

valuation ratio of one ļ¬rm to the other ļ¬rm, you would have concluded that PepsiCo and Coca

Cola are not so similar, after all, and that you should not have compared the two. You just got

lucky. You lived in ignorant bliss.

Solve Now!

Q 10.5 List the main problems with using comparables.

Q 10.6 A ļ¬rm with a P/E ratio of 20 wants to take over a ļ¬rm half its size with a P/E ratio of 50.

What will be the P/E ratio of the merged ļ¬rm?

Q 10.7 The following are quarterly earnings and assets for Coca Cola and PepsiCo:

KO PEP

Earnings (Qua/Ann) Assets (Qua/Ann) Earnings (Qua/Ann) Assets (Qua/Ann)

6/2002 1,290 25,287 888 24,200

3/2002 801 23,689 651 22,611

12/2001 914 3,979 22,417 22,417 667 2,662 21,695 21,695

9/2001 1,074 22,665 627 23,036

6/2001 1,118 22,387 798 19,503

3/2001 873 22,248 570 18,660

12/2000 242 2,177 20,834 20,834 698 2,183 18,339 18,339

9/2000 1,067 23,141 755 17,659

6/2000 926 23,258 668 17,492

If it is now in July 2002, what would be good comparable earnings and comparable assets for

these two ļ¬rms?

Q 10.8 A ļ¬rm that is 100% equity ļ¬nanced is considering a recapitalization to a 50-50 debt-

equity ratio. What will happen to its P/E ratio?

Q 10.9 A ļ¬rm has a P/E ratio of 12 and a debt-equity ratio of 66%. What would its unlevered

P/E ratio (i.e., the P/E ratio of its underlying business) approximately be?

Q 10.10 On October 9, 2002, the seven auto manufacturers publicly traded in the U.S. were

Manufacturer Market Cap Earnings

Volvo (ADR) $5.7 ā“$0.18

Ford $14.1 ā“$5.30

GM $18.8 $1.83

Nissan (ADR) $27.0 $2.55

DaimlerChrysler $32.3 $4.63

ļ¬le=comparables.tex: RP

255

Section 10Ā·4. Other Financial Ratios.

(All quoted dollars are in billions. Ignore leverage. ADR means American Depositary Receipt, a

method by which foreign companies can list on the New York Stock Exchange.) On the same day,

Yahoo! Deutschland reported that Volkswagen AG had earnings of 3.8 billion euro. In terms of

sales, Volkswagen was most similar to Volvo and Ford. What would you expect Volkswagen to be

worth?

Q 10.11 What are the basic assumptions in applying the P/E ratio of one company to the earnings

of another company?

10Ā·4. Other Financial Ratios

Financial ratio analysis is extremely widely used in the real worldā”unfortunately, often without

a good understanding of what ratios mean, what they do not mean, how they can be put to good

use, and how they can sometimes obscure the right decision. If you do ļ¬nancial ratio analysis,

be very, very careful. Know what it is that you are doing and think about meaning.

You should now understand that price-earnings ratios are very useful, but they are no panacea.

They have big shortcomings, too. Still, overall, the P/E ratio is the best ratio I am aware of.

However, there are situations in which other value ratios can give you better value estimates.

Moreover, there are non-value based ratios, whose purpose is less to give you an estimate of

value and more to give you intuition about the economics of the ļ¬rm.

10Ā·4.A. Value-Based Ratios

There are a large number of other ratios in use, and this section presents a potpourri of some Price-earnings ratios are

not the only measure.

popular ones. The list is not exhaustive, as indeed only the imagination limits the quantities

The goal is to ļ¬nd a

that can be used in the denominator. Two ratios that are relatively similar to the P/E ratio measure that is

discussed in the previous section are proportional to value.

Alternative Price-Earnings or Cash Flow Ratios Earnings can be deļ¬ned in a variety of ways:

with or without extraordinary items, diluted, etc. There is no right or wrong way: the goal

is to ļ¬nd a ratio that makes the comparables ļ¬rm appear to be as similar as possible.

For example, one measure of earnings that from Chapter 9 is EBITDA (earnings before

interest and taxes, depreciation, and amortization). The rationale is that accounting de-

preciation is so ļ¬ctional that it should not be subtracted out. But EBITDA has problems

with leverage (interest expense) and capital expendituresā”if you use it, please subtract

these. Of course, if you do, you will de-facto use a price over cash ļ¬‚ow ratio, which can

suļ¬er from the shortcomings that capital expenditures are very ālumpy.ā This is why we

used earnings rather than cash ļ¬‚ows in the ļ¬rst place.

Price/Book-Value-of-Equity Ratios This ratio is commonly used, and often abbreviated as the

market/book ratio. It should not be recommended for valuation purposes. The reason

is that the book value of equity is often close to meaningless. Accountants use the book

value of equity to balance assets and liabilities, in accordance with all sorts of accounting

conventions (such as depreciation). As a result, this measure is especially diļ¬erent across

ļ¬rms with diļ¬erent ages of ļ¬xed assets (such as buildings).

However, sometimes neither earnings nor the book-value of equity are meaningful. For exam- Many biotech ļ¬rms have

neither earnings nor

ple, biotech ļ¬rms may need to be valued even before they have meaningful, positive earnings.

sales. So, what to use?

The idea is to substitute another, more meaningful quantity for earnings. In biotech ļ¬rms, a

better (but still very bad) measure than earnings may be the number of scientists. An ana-

lyst might ļ¬nd that biotech ļ¬rms are worth $1,000,000 per employed scientist. In principle,

the comparables valuation method remains the same as it was when used with price earnings

ratios. The alternative ratio typically still has price (either equity value or overall ļ¬rm value)

ļ¬le=comparables.tex: LP

256 Chapter 10. Valuation From Comparables.

in the numerator, but a quantity other than earnings (e.g., sales or number of scientists) in

the denominator. The analyst chooses comparable ļ¬rm(s), determines an appropriate typical

comparables ratio, and ļ¬nally multiplies this comparables ratio by the ļ¬rmā™s own quantity to

determine its value. This may work well only if ļ¬rms are comparable enough among the chosen

dimensions that application of the ratio of some ļ¬rms to the ratio of others oļ¬ers a meaningful

price.

Price/Sales Ratios This ratio is especially popular for industries that do not have positive earn-

ings. Therefore, it was commonly used during the Internet bubble, when few Internet ļ¬rms

had positive earnings. Presumably, ļ¬rms with higher sales should be worth more.

One problem was that ļ¬rms, such as Amazon during the Internet bubble at the turn of

the millennium, were known to sell merchandise at a loss. Naturally, it is relatively easy

to sell $100 bills for $99! So, the more Amazon sold, the more money it lostā”but the

more valuable Amazon appeared to be. After all, with higher sales, the Price/Sales ratio

suggested that Amazon would be worth more.

Price/Employees Ratio This ratio is popular when ļ¬nancials are deemed not trustworthy. Of

course, it assumes that the employees at the comparable ļ¬rm are as productive as the

employees in the company to be valued.

Price/Scientists Ratio This ratio is popular for upstart technology ļ¬rms, which have neither

earnings nor sales. One problem is that it induces ļ¬rms to hire incompetent scientists on

the cheap in order to increase their valuations. After all, ļ¬rms with more scientists are

presumed to be worth more.

Price/Anything Else Your imagination is the limit.

This latter set of ratios only makes sense if you compute them for the enterprise value of the

ļ¬rm (that is, the value of all equity plus the value of all debt). If you want to obtain the value

of the equity, you should compute these ratios using the enterprise value, and then subtract

oļ¬ the current value of all debt.

Solve Now!

Q 10.12 On July 28, 2003 (all quoted dollars are in billions):

Firm Cash Sales Dividends Value D/E

CSG n/a $9.2 $0.4 $12.2 153%

KO $3.6 $20.3 $2.2 $110.8 43%

PEP $1.8 $25.9 $1.1 $81.0 22%

Hansen Natural had $210,000 in cash, $9.22 million in sales, zero dividends, and a debt/equity

ratio of 10%. What would a price/cash ratio predict its value to be? A price/sales ratio? A

price/dividend ratio? Elaborate on some shortcomings.

ļ¬le=comparables.tex: RP

257

Section 10Ā·4. Other Financial Ratios.

10Ā·4.B. Non-Value-Based Ratios Used in Corporate Analyses

Not all ratios are used to estimate ļ¬rm value. Other ratios can help to assess ļ¬nancial health Other ratios can be used

to judge health and

and proļ¬tabilityā”or can be merely interesting. They can help in the āartā of valuation if they

proļ¬tability.

can help you learn more about the economics of the ļ¬rm. For example, a number of ratios are

often used to judge ļ¬nancial health (proximity to bankruptcy) and proļ¬tability. Most ratios vary

systematically by industry and over the business cycle. Thus, they should only be compared to

similar ļ¬rms at the same time. On occasion, however, ratios can be so extreme that they can

raise a good warning ļ¬‚ag. For example, if you ļ¬nd that the ļ¬rm has ten times its earnings in

interest to pay, you might become somewhat concerned about the possibility of bankruptcy,

regardless of what is standard in the industry at the time.

Before discussing the ratios, realize that you should be twice as cautious when ratios involve Watch out for the

meaning of book value

quantities from the balance sheet and four times as cautious when they involve the book value

of equity, in particular.

of equity. This quantity is often so far from the true market value that ratios based on the book

value can be almost meaningless. (It is not even a good estimate of replacement value, either.)

The reason is that after accountants have completed all their bookkeeping, this number will

become what is required to equalize the left-hand side and right-hand side of the balance sheet.

It is a āplaceholder.ā

Without further ado, here are some of the more interesting and common ratios. For each one, We now do ratios on

PepsiCo.

you will ļ¬nd one or more sample computations for PepsiCo in 2001 (which you can compare to

the ļ¬nancials from Section 9Ā·1.B), but be aware that many of these ratios exist in various forms.

The ratios are sorted, so that the ones at the top tend to reļ¬‚ect ļ¬nancial health and liquidity,

while the ones at the bottom tend to reļ¬‚ect proļ¬tability. www.investopedia.com oļ¬ers a nice

reference for many of these ratios.

Let us begin with ratios that consider the ļ¬rmā™s debt load. A ļ¬rm that has high debt ratios Debt-related ratios.

(especially compared to its industry) must often be especially careful to manage its cash and

inļ¬‚ows well, so as to avoid a credit crunch. Moreover, if you want to borrow more money, then

potential new creditors will be very interested in how likely it is that you will not default. They

will judge your indebtness relative to your proļ¬tability, cash ļ¬‚ow, and industry.

Debt/Equity Ratio The ratio of debt over equity. Many variations exist: debt can be just long-

term debt, all obligations, or any other kind of liability. Equity can be measured either in

terms of book value or in terms of market value.

Long Term Debt 2, 651

= ā 3% . (10.29)

PepsiCo, 2001:

Market Value of Equity 87, 407

Long Term Debt 2, 651

= ā 31% . (10.30)

PepsiCo, 2001:

Book Value of Equity 8, 648

As stated above, the book value of equity is very problematic. The book value of debt is

usually much betterā”and, as is not the case with equity, you rarely have access to the

market value of debt, anyway. (If interest rates have not changed dramatically since issue,

this is a good approximation of overall market value.)

All Liabilities 13, 047

= ā 15% . (10.31)

PepsiCo, 2001:

Market Value of Equity 87, 407

Debt Ratio As above, but adds the value of debt to the denominator. Because market value of

debt is rarely available, a common variant adds the book value of debt and the market

value of equity. For example,

Long Term Debt 2, 651

= ā 2.6% . (10.32)

PepsiCo, 2001:

87, 407 + 13, 047

Market Value of Equity + Debt

Long Term Debt 2, 651

= ā 12% . (10.33)

PepsiCo, 2001:

Book Value of Assets 21, 695

ļ¬le=comparables.tex: LP

258 Chapter 10. Valuation From Comparables.

All Liabilities 13, 047

= ā 13% . (10.34)

PepsiCo, 2001:

87, 407 + 13, 047

Market Value of Equity + Debt

Interest Coverage The ratio of debt payments due as a fraction of cash ļ¬‚ows. Many variations

exist: debt payments can be only interest due, or include both principal and interest. Cash

ļ¬‚ows can be any of a number of choices. Popular choices are pure cash ļ¬‚ows, operating

cash ļ¬‚ows, net income plus depreciation minus capital expenditures, and net income plus

depreciation. For example,

Short Term Borrowings 354

= ā 23% . (10.35)

PepsiCo, 2001:

Cash Flow (Table 9.10) 1, 556

Times Interest Earned (TIE) The earnings before interest (usually also before taxes) divided

by the ļ¬rmā™s interest. In some sense, the inverse of interest coverage.

Times Interest Earned 4, 021

(10.36)

= ā 18 .

PepsiCo, 2001:

TIE 219

Current Ratio The ratio of current assets (cash, accounts receivables, inventory, marketable

securities, etc.) over current liabilities (interest soon-due, accounts payable, short-term

loans payable, etc.) is a measure of liquidity. Often interpreted to be āhealthyā if greater

than 1.5.

Current Assets (Page 217) 74

(10.37)

= ā 0.5 .

PepsiCo, 2001:

Current Liabilities 158

Do not read too much into this ratio. PepsiCo is very healthy, even though its current

ratio is low.

Quick Ratio or Acid-Test is like the current ratio, but deletes inventories from current assets.

It is often considered healthy if it is greater than 1.0. The idea is that you are then likely

to be able to cover immediate expenses with immediate income.

Current Assets (Page 217) 7

(10.38)

= ā 0.0 .

PepsiCo, 2001:

Current Liabilities 158

The cash ratio further eliminates receivables from current assets.

Duration and Maturity You have already used these concepts in the bond context, but they

can also apply to projects and even to ļ¬rms. They can measure what type of investment

the ļ¬rm is really makingā”short-term or long-term. This is not an ordinary ratio in that it

requires projections of future cash ļ¬‚ows.

Turnover The ratio of sales divided by a component of working capital.

ā¢ Inventory Turnoverā”how often your inventories translate into sales.

Net Sales 26, 935

= ā 21/year . (10.39)

PepsiCo, 2001:

Inventories 1, 310

Most ļ¬nancials also provide the components of inventories, so you could further

decompose this.

ā¢ Receivables Turnoverā”how quickly your customers are paying.

Net Sales 26, 935

= ā 13/year . (10.40)

PepsiCo, 2001:

Receivables 2, 142

ļ¬le=comparables.tex: RP

259

Section 10Ā·4. Other Financial Ratios.

ā¢ Payables Turnoverā”how quickly you are paying your suppliers.

Net Sales 26, 935

= ā 6/year . (10.41)

PepsiCo, 2001:

Payables 4, 461

These measures are sometimes inverted (one divided by the ratio) and multiplied by 365

to obtain a ānumber of daysā measure. For example,

ā¢ Days of Receivables Outstanding (DRO), also called Days of Sales Outstanding

(DSO). Accounts Receivables divided by total sales on credit, times number of days

outstanding.

365 Ā· Receivables 365 Ā· 2, 142

= ā 29 days . (10.42)

PepsiCo, 2001:

Net Sales 26, 935

PepsiCo collects its bills about every 30 days. A lengthening of this number often

indicates that customers are running into ļ¬nancial diļ¬culties, which could impact

PepsiCo negatively.

ā¢ Days of Inventories Outstanding. Inventory divided by total sales on credit, times

number of days outstanding:

365 Ā· Inventories 365 Ā· 1, 310

= ā 18 days . (10.43)

PepsiCo, 2001:

Net Sales 26, 935

PepsiCo turns over its inventory every 18 days.

ā¢ Days of Payables Outstanding (DPO). Accounts Payables divided by total sales on

credit, times number of days outstanding.

365 Ā· Payables 365 Ā· 4, 461

= ā 60 days . (10.44)

PepsiCo, 2001:

Net Sales 26, 935

A lengthening of this number could mean that PepsiCo is having diļ¬culties coming

up with cash to meet its ļ¬nancial obligationsā”or found a way to pay bills more

eļ¬ciently (more slowly in this case).

There are also combined versions, such as the Cash Conversion Cycle, which is the sum

of inventory processing period and the number of days needed to collect receivables. For

PepsiCo, this would be 18 + 29, or about one-and-a-half months.

Turnover ratios and their derivatives (below) are especially important for ļ¬rms in the

commodities and retail sector, such as Wal-Mart. Good control often allows ļ¬rms to

leverage economies-of-scale. In this sense, the above measure corporate eļ¬ciency, and

help managers judge their own eļ¬ciency relative to their competition.

Proļ¬t Margin (PM) or Return on Sales The net or gross proļ¬t divided by sales.

Net Income 2, 662

= ā 10% . (10.45)

PepsiCo, 2001:

Sales 26, 935

Mature cash cow ļ¬rms should have high ratios; growth ļ¬rms typically have low or negative

ratios.

Return on (Book) Assets (ROA), like return on sales, but divides net income by the book value

of assets.

Net Income 2, 662

= ā 12% . (10.46)

PepsiCo, 2001:

Book Value of Assets 21, 695

A variant of this measure that adds back interest expense is better, because it recognizes

that assets pay out cash to both shareholders and creditors. Nevertheless, both measures

are dubious, because the book value of assets is often very unreliable. (The book value of

assets contains the book value of equity.)

ļ¬le=comparables.tex: LP

260 Chapter 10. Valuation From Comparables.

Return on (Book) Equity (ROE), like return on sales, but divides net income by the book value

of equity. You also know that I really do not like this measure.

Net Income 2, 662

= ā 31% . (10.47)

PepsiCo, 2001:

Book Value of Equity 8, 648

Total Asset Turnover (TAT) A measure of how much in assets is required to produce sales.

Again, with book value of assets in the denominator, this is not a reliable ratio.

Sales 26, 935

= ā 1.2 . (10.48)

PepsiCo, 2001:

Assets 21, 695

The DuPont Model multiplies and divides a few more quantities into the deļ¬nitions of ROA

and ROE:

Net Income Net Income Assets Sales

ROE = = Ā· Ā·

Book Equity Sales Book Equity Assets

(10.49)

Asset Turnover

Proļ¬t Margin Equity Multiplier

Net Income EBIT - Taxes Net Income Assets Sales

= Ā· Ā· Ā· Ā· .

EBIT - Taxes Sales Sales Book Equity Assets

A similar operation can be applied to a variant of ROA:

EBIAT EBIAT Sales

(10.50)

ROA = = Ā· .

Assets Sales Assets

EBIAT is net income before interest after taxes. With book value of assets and book

equity involved, this is often not a particularly trustworthy decomposition, even though

it is mathematically a tautology.

The idea of these decompositions is that they are supposed to help you think about what

the drivers of ROE and ROA are. Again, I do not like this analysis, because I believe that

neither ROA nor ROE are good starting points for an analysis of what drives value. Not

everyone agrees with my opinion hereā”especially not the individuals administering the

CFA exam, where the DuPont model remains a staple.

Book-to-Market Ratio The book-value of the equity divided by the market value of the equity.

If the book value of equity is representative of how much the assets would cost to replace,

then this is a measure of how much the market values the (special) growth opportunities

that the company has created from replaceable assets.

Book Equity 8, 648

= ā 10% . (10.51)

PepsiCo, 2001:

Market Equity 87, 407

Dividend Payout Ratio The paid out dividends divided by earnings. The idea is that a ļ¬rms

that pays out more earnings today should pay out less in the future, becauseā”in contrast

to a ļ¬rm that retains earningsā”it lacks the paid out cash for reinvestment.

Dividends 994

= ā 37% . (10.52)

PepsiCo, 2001:

Net Income 2, 662

Payout Ratio The dividend payout ratio can be broadened to also include share repurchases,

or even net repurchases (i.e., net of equity issuing) to obtain a net payout ratio.

Dividends + Equity Repurchasing 2, 710

= ā 100% . (10.53)

PepsiCo, 2001:

Net Income 2, 662

Dividends + Equity Repurchasing - Issuing 2, 186

= ā 82% . (10.54)

PepsiCo, 2001:

Net Income 2, 662

ļ¬le=comparables.tex: RP

261

Section 10Ā·4. Other Financial Ratios.

PepsiCo distributed most of its earnings to shareholders.

Dividend Yield The amount of dividends divided by the share price. Dividends can include

share repurchases (in which case, this is called the payout ratio). Dividends are a ļ¬‚ow

measure, while the stock price is a stock measure. Consequently, dividends can be mea-

sured at the beginning of the period or at the end of the period (in which case, this is called

the dividend-price ratio). Incidentally, stock-ļ¬‚ow timing was also an issue for some of

the measures above, though timing matters more for volatile measures, such as the stock

market value. For example,

Dividends + Equity Repurchasing 2, 710

= ā 3.1% . (10.55)

PepsiCo, 2001:

Market Value 87, 407

Firms that have a low payout yield today either have to see smaller stock price increases

in the future (which means a lower expected rate of return), or they have to increase their

payout yield sometime in the future. Otherwise, no one would want to hold them today.

Retention Ratios The retained earnings, divided either by sales, assets, or income. A ļ¬rm that

decides to start retaining more earnings should pay out more in the future. Because the

retained earnings should be reinvested, such ļ¬rms should have higher expected earnings

growth. These measures are usually calculated as one minus the dividend payout ratio

or one minus the sum of dividends and equity repurchases divided by net income or

one minus the sum of dividends and net equity repurchases divided by net income. For

example,

2, 662 ā’ 2, 710

Net Income - Payout

= ā ā’0% . (10.56)

PepsiCo, 2001:

Payout 2662

PepsiCo also issued $524 of shares in connection with the Quaker merger, so

2, 662 ā’ 2, 710 + 524

Net Income - Net Payout

= ā 19% . (10.57)

PepsiCo, 2001:

Net Payout 2, 662

so its retention rate could be judged to be around 19%.

How useful are these ratios? It depends on the situation, the industry, and the particular ratio

for the particular ļ¬rmā”and what you plan to learn from them. If every ļ¬rm in the industry

has almost the same ratio, e.g., a days of receivables average somewhere between 25 and 32

days, and the ļ¬rm you are considering investing in reports 7 days, you should wonder about

the economics of this shorter number. Is your ļ¬rm better in obtaining money quickly? Does

it do so by giving rebates to faster paying customers? Does it mostly work on a cash basis,

while other ļ¬rms in the industry work on credit? If so, why? Or is your ļ¬rm simply cooking its

books?

ļ¬le=comparables.tex: LP

262 Chapter 10. Valuation From Comparables.

Closing Thoughts: Comparables or NPV?

10Ā·5.

Should you use comparables or net present value? In practice, comparables enjoy great pop-

Use both valuation

methods, and use ularity, primarily because they do not require much thought. Anyone can look up another

common sense to decide

ļ¬rmā™s P/E ratio and multiply it by the earnings of our own ļ¬rm. In contrast, even a rough NPV

what you believe.

analysis is quite involved. Of course, after reading this chapter, you should understand that

both methods rely on inputs that you will almost surely not know perfectly. You will never

have the perfect comparable, and you will never know the expected future cash ļ¬‚ow perfectly.

Fortunately, the cause of errors is diļ¬erent for these two methods. Therefore, if you use both,

you can get a better idea of where the true value lies. This does not mean that you should aver-

age the valuation estimates obtained from NPV and comparables. Instead, you should perform

both analyses, and then take a step back and make up your mind as to which combination of

methods seems to make most sense in your particular situation.

Yes, valuation is as much an art as it is a science. It consists of the tools that you have now

learned and your ability to judge. If you can judge better than others, you will end up a rich

person.

10Ā·6. Summary

The chapter covered the following major points:

ā¢ The P/E ratio (price-earnings) is the price of the ļ¬rm divided by the ļ¬rmā™s earnings, or

equivalently the share price divided by the earnings per share.

Often, these earnings are not the current but the expected earnings.

ā¢ The P/E ratio reļ¬‚ects the ļ¬rmā™s growth opportunities and cost of capital. Higher growth

ļ¬rms have higher P/E ratios.

ā¢ P/E ratios and other methods based on comparables can provide an alternative valuation

of ļ¬rms and projects.

ā¢ Comparables suļ¬er from a variety of problems, some of which can be corrected, and some

of which are intrinsic and uncorrectable.

ā¢ Never average P/E ratios. Either average E/P yields and then invert, or divide total multiple-

ļ¬rm values by total multiple-ļ¬rm earnings.

ā¢ The comparables valuation techniques and NPV have diļ¬erent weaknesses, which there-

fore often makes it worthwhile to consider and judge both.

ā¢ There are many other ratios that can be used to judge the proļ¬tability and the ļ¬nancial

health of a company. As far as valuation is concerned, their primary purpose is only to

provide useful background information.

ļ¬le=comparables.tex: RP

263

Section A. Advanced Appendix: A Formula For Unlevering P/E ratios.

Appendix

A. Advanced Appendix: A Formula For Unlevering P/E ratios

Return to the example in Section 10Ā·2. Your comparison benchmark ļ¬rm was Start with a special case

in which ļ¬rms have

comparable leverage.

P/E

E P

Firm B Financing

100-0 Equity-Debt Financed $100.00 $1,000 10

50-50 Equity-Debt Financed $62.50 $500 8

So, here is your problem: How do you value ļ¬rm A, if the underlying projects of ļ¬rm A are

similar to those of ļ¬rm B? Should you use 8 or 10 as your price-earnings ratio? The answer

is easy if A has the same debt equity ratio as B. Then you can just use the comparison ļ¬rmā™s

price equity ratio as a proxy for your own price equity ratio. That is, if Firm A produced $200

in income for equity holders each year, after ļ¬nancing with a 50/50 debt equity ratio, then you

would expect its equity value to be about

Price

Implied A Value = Ā· EarningsA

Earnings A

Price

ā Ā· EarningsA

Earnings B

= 8 Ā· $200 = $1, 600 ,

where we write out Earnings to avoid confusion with equity. As just stated, this equity valuation

depends on the assumption that Firm A had borrowed an equal amount in outstanding debt

($1,600), i.e., that it had a 50/50 debt equity ratio to which you could apply your B multiple.

But what do you do if your A, with its reported income of $200 for equity holders, had borrowed Problem is: leverage may

be different. Try to

$2,500 instead of $1,600? Or, what if A had not borrowed anything? You need to determine an

unlever both.

appropriate comparable that you can apply to A and that takes into account the actual leverage

of A and of B. The easiest method is to convert all price-earnings ratios to a 0/100 debt equity

ratio. In this case, you already know the result that you wish to obtain: a formula should tell

you that unlevering B should translate the previous ratio of 8 into a price-earnings ratio of 10.

Next, you need to look up the interest rate that A is paying for borrowing. Let us assume that

Aā™s records inform you that the interest rate is 8%. This means that A is paying $200 in interest

each year, before it paid oļ¬ the $200 to its equity holders. Consequently, you know that a

0/100 debt equity A would have produced earnings of $200 + $200 = $400. Thus,

Price

Implied A Value = Ā· EarningsA

Earnings A

Price

ā Ā· EarningsA

Earnings B

= 10 Ā· $400 = $4, 000

This would be the value of an all equity ļ¬rm. Because A has borrowed $2,500, its equity must

be worth $1,500.

ļ¬le=comparables.tex: LP

264 Chapter 10. Valuation From Comparables.

So the trick is to convert all debt equity ratios into āall equityā ratios ļ¬rst. Unfortunately, there

An attempt at a

delevering formula. is no general formula to do so: the translation formula depends on the time when the cash

ļ¬‚ows are likely to occur. The following formula, based on a plain perpetuity assumption on

the ļ¬rmā™s earnings, often works reasonably well:

A Debt Adjustment Formula for P/E ratios

Debt

1 ā’ (rFirm ā’ rDebt ) Ā·

Price Earnings

=

rFirm

Earnings Relevered

Debt PriceFirm

= 1 ā’ (rFirm ā’ rDebt ) Ā· Ā·

Earnings EarningsFirm

where āļ¬rmā means an all-equity no-debt ļ¬nanced ļ¬rm. Let us apply this formula to ļ¬rm B. Let

us assume that you know that B has a value of $1,000 and a price-earnings ratio of 10 when

it has no debt, but it is now considering a move to a 50/50 debt equity ratio. You want to

determine this capital structure change on its new price-earnings ratio. Use the formula:

Price Debt PriceFirm

= 1 ā’ (rFirm ā’ rDebt ) Ā· Ā·

Earnings Earnings EarningsFirm

Relevered

$500

= 1 ā’ (10% ā’ 7.5%) Ā· Ā· 10

$62.50

= [1 ā’ 0.025% Ā· 8] Ā· 10

= 0.8 Ā· 10 = 8 .

This formula makes it easy to ļ¬gure out how an all equity ļ¬rmā™s price earnings ratio changes

when it takes on debt. If you know the debt equity ratio of a ļ¬rm and want to convert it into a

debt-free equivalent price-earnings ratio, then you can use the following conversion.

To convert the observed leveraged P/E ratio into a hypothetical P/E ratio for an unlevered ļ¬rm,

the following approximation formula can be helpful:

Price

Earnings Firm

(10.58)

1 Price

= Ā· .

Debt Earnings

1 ā’ (rFirm ā’ rDebt ) Ā· Equity

Earnings

This formula makes very speciļ¬c assumptions on the type of ļ¬rm, speciļ¬cally that earnings

are a plain perpetuity. The formula can sometimes be a decent approximation if earnings are

not a perpetuity.

ļ¬le=comparables.tex: RP

265

Section A. Advanced Appendix: A Formula For Unlevering P/E ratios.

Solutions and Exercises

1. You would probably value houses by the method of compsā”NPV would be exceedingly diļ¬cult to do. How-

ever, there are often similar houses that have recently sold. You might use a ratio that has price in the numer-

ator and square-foot in the denominator, and multiply this ratio from comparable houses by the square-foot

of your new residence.

2. Microsoft is growing faster, so it would have a higher P/E ratio.

3. E/P = E (Ė) ā’ E (g) ā’ E (Ė) = P /E + E (g) = 1/40 + 6% = 8.5%. Therefore, E/P = 8.5% ā’ 7% = 1.5% and its

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Ė Ė

P/E ratio would shoot from 40 to 66.7. The percent change in value would therefore be 66.6/40 ā’ 1 ā 66%.

4. E/P = E (Ė) ā’ E (g) ā’ E (g) = E (Ė) ā’ E/P = 10% ā’ 1/20 = 5%.

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Ė Ė

5. See the text.

6. Do an example. The acquirer has value of $100, so it needs to have earnings of $5. The target has value of

$50, so it needs to have earnings of $1. This means that the combined ļ¬rm will have earnings of $6 and value

of $150. Its P/E ratio will thus be 25.

7. Earnings: The TTM Earnings for KO is 3, 979 + (801 ā’ 873) + (1, 290 ā’ 1, 118) = 4, 079. The TTM Earnings

for PEP is 2, 662 + (651 ā’ 570) + (888 ā’ 798) = 2, 833. Assets: You would not compute a TTM, but use the

most recent assets: $25,287 for Coca-Cola and $24,200 for Pepsico.

8. You know from the text that the P/E ratio would go down.

9. This question cannot be answered if you do not know the diļ¬erent costs of capital. For example, if the ļ¬rmā™s

cost of capital is equal to the debt cost of capital, the P/E ratio would not change at all!

Yahoo reported an actual market value of $10.52 billion euros, and an earnings yield of 36.9% (P/E of 2.7).

10.

The easy part is supplementing the table:

Manufacturer Market Cap Earnings P/E ratio E/P yield

Volvo (ADR) $5.7 ā“$0.18 ā“31.7 ā“3.2%

Ford $14.1 ā“$5.30 ā“2.7 ā“37.6%

GM $18.8 $1.83 10.3 9.7%

Nissan (ADR) $27.0 $2.55 10.6 9.4%

DaimlerChrysler $32.3 $4.63 7.0 14.3%

Honda (ADR) $37.7 $3.09 12.2 8.2%

Toyota (ADR) $87.3 $4.51 19.4 5.2%

Sum $222.9 $11.13 25.1 6.0%

Average $31.8 $1.59 3.6 0.9%

The hard part is deciding on a suitable P/E comparable. The ļ¬rst method (average E/P yield, then invert)

suggests adopting the astronomical ratio of 1/0.9% = 111, due to Fordā™s enormous loss in terms of market

capitalization (Ford had $85 billion in sales, and a positive EBITDA of $4.8 billion. But Ford also has ongoing

depreciation on the order of $15 billion per year, but capital and other expenditures on the order of $18 (2001)

to $37 billion (2000 and 1999).) The second method (sum up Eā™s and Pā™s ļ¬rst) suggests $222.9/$11.1 = 20,

but it weighs the larger [and Japanese] ļ¬rms more highly. Nevertheless, in this case, the second method came

closer to the actual Volkswagen P/E multiple of 27.

Incidentally, by mid-2003, VW had introduced a couple of ļ¬‚ops, and its earnings had sagged to $2.5 billion,

though its market capitalization had increased to $15 billion. This meant that Volkswagenā™s P/E multiple had

shrunk from 27 to 6 in just nine months!

11. The ļ¬rms are alike substitutes in all respects, including product, product lines, and debt ratio.

12. These ratios are usually performed without debt adjustmentā”the equivalent of surgery without anesthesia.

This is a huge problem, but it also makes this exercise relatively easy.

Firm Value/Cash Value/Sales Value/Dividends

CSG n/a 1.3 30

KO 185 5.5 50

PEP 45 3.1 74

ā¢ The cash-based ratio suggests a value between $10 million and $39 million. The cash-based ratio values

all ļ¬rms as if only current cash has any meaning, and the ongoing operations are irrelevant (except to

the extent that they have inļ¬‚uenced current cash).

ļ¬le=comparables.tex: LP

266 Chapter 10. Valuation From Comparables.

ā¢ The sales-based ratio suggests a value between $12 million, $29 million, and $50.6 million. Because the

smaller comparables have lower ratios, one might settle on a lower value. The sales-based ratio ignores

that CSGā™s equity value is relatively low because more of its value is capitalized with debt than with

equity.

ā¢ The dividend-based ratio suggests a zero value. Obviously, this is not a perfect estimate. Firms can

choose diļ¬erent payout policies.

Hansenā™s actual value on this day was $51.4 million.

(All answers should be treated as suspect. They have only been sketched, and not been checked.)

Part III

Investments

There is a long version and short version of the Investments part of the book. You are looking at the long version.

The short version will appear in a dedicated corporate ļ¬nance version of the book, and can already be downloaded

from the website.

This introduction appears in the Survey text only.

267

269

Transition

We are still plagued by one problem: We do not yet know where the cost of

capital, the E(Ė), in the present value formula comes from. We just assumed

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we knew it.

In the real world, the cost of capital is determined by our investorsā”and our

investors have many choices. So we have to understand their mindset. They

can put money in bonds, stocks, projects, etc.ā”or into our ļ¬rmā™s projects. If

investors very much like the alternatives, then our ļ¬rmā™s cost of capital will

be high. Think of our corporate cost of capital as our investorsā™ Opportunity

Cost of Capital.

To learn more about where the cost of capital comes from, we have to study

not just our own project, but more generally how investors thinkā”what they

like and dislike.

Of course, it is nice that we are often ourselves investors, so learning how to

best invest money in the ļ¬nancial markets has some nice side beneļ¬ts.

ńņš. 13 |